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feature is included, and represents the decision values for the particular transaction
TID
and object
OID
.
Mining meta-actions transformations requires the study of the transactional
datasets in hand. Commonly, transactional datasets do not represent the objects tem-
poral transformations resulting from applying meta-actions. To be able to mine meta-
action's transformations (atomic action terms), objects have to be uniquely identified
along with their transactions and clustered by their identifier. Object's transactions
should be ordered based on temporal sequential order. Every two sequential object's
transactions will be paired for every meta-action based on a temporal precedence
relationship. The resulting pairwise partition will model the atomic action terms tran-
sitions for each object given the meta-action applied. For instance, given a patient
visits recorded in our dataset with high blood pressure, high fever, and headaches for
his first visit to the doctor, who gave him/her a treatment
m
, at the second visit the
patient diagnosis displays no fever, high blood pressure and no headache. In such a
case we can extract the following atomic action terms for this patient pair of visits:
(
fever
,
high
ₒ
no
)
,
(
blood pressure
,
high
ₒ
high
)
,
(
headaches
,
yes
ₒ
no
)
.
Now, we introduce the set of transactions
T
. Let us assume that
S
=
(
X
,
F
∪
{
is a decision system, where
X
is a set of objects,
F
is a set of classifi-
cation attributes,
d
is the decision attribute, and
V
is a set of values of attributes
in
F
d
}
,
V
)
∪{
d
}
, such that
f
(
X
)
ↆ
V
, for any
f
∈
F
. Also, let us assume that
M
(
S
)
is a set of meta-actions associated with
S
. In addition, we define the set
{
s
i
,
j
:
j
∈
J
i
}
of ordered transactions
J
i
associated with
x
i
∈
X
, such that
=[
(
x
i
,
(
x
i
)
j
)
]
(
∀
,
)
[
∈
]
(
x
i
)
j
is defined as the
s
i
,
j
F
, where
i
j
s
i
,
j
T
.Theset
F
{
(
x
i
)
:
∈
}
set of attribute values
of the object
x
i
in the transaction uniquely
represented by the transaction identifier
j
. Each transaction represents the current
state of the object when recorded with respect to a temporal order based on
j
for all
s
i
,
j
f
f
F
T
.
We define a precedence relationship denoted as
∈
>
p
on the system
S
to help locate
the position of each transaction within each object's ordered transaction set. Given
two transactions
s
i
,
j
and
s
i
,
k
for an object
x
i
X
, the precedence relationship
s
i
,
j
>
p
s
i
,
k
represents the order of the recorded transactions for the object
x
i
, and
says that the transaction
s
i
,
j
was recorded before the transaction
s
i
,
k
.
To strengthen this relationship, we define the set
P
∈
(
S
)
of pairs
(
s
i
,
j
,
s
i
,
k
)
such
that
if and only if
s
i
,
k
occurred directly after
s
i
,
j
(there is no other
transaction between them in the system
S
).
It should be observed that any pair
(
s
i
,
j
,
s
i
,
k
)
∈
P
(
S
)
(
s
i
,
j
,
s
i
,
k
)
=
(
[
(
x
i
,
F
(
x
i
)
j
)
]
,
[
(
x
i
,
F
(
x
i
)
k
)
]
)
in
P
.
We assume that there is always a set of meta-actions in
M
applied before any
transaction
s
i
,
k
with the exception of the very first transaction
s
i
,
1
for each object
x
i
(
S
)
represents a set of atomic action terms
{
(
f
,
f
(
x
i
)
j
ₒ
f
(
x
i
)
k
)
:
f
∈
F
}
∈
X
. This suggests that the transaction
s
i
,
k
in the pair (
s
i
,
j
,
s
i
,
k
) is a direct
consequence of applying some set of meta-actions
m
(
m
X
,
and supports the assumption that the state of the objet
x
i
is being affected by these
meta-actions.
As we already observed, each transaction pair
ↂ
M
) to the object
x
i
∈
(
s
i
,
j
,
s
i
,
k
)
encompasses the set of
{
(
,
(
x
i
)
j
ₒ
(
x
i
)
k
)
:
∈
}
atomic action terms
A
j
,
k
of the form
f
f
f
f
F
, that defines
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